Quantum Field Theory of Many-Body Systems

Lecture (MVSpec)

Thomas Gasenzer

Tuesday, 11:15-13:00; Thursday, 11:15-13:00; INF 227 (KIP), SR 1.404. [LSF]

Tutor: Markus Karl

Register and view group list here.
Classes take place on Fridays, 14:15-15:45 hrs, starting on 24/10: INF 227 (KIP), HS 2.

Written exam on Tue., 10/02/15, 10:00-12:00 hrs, INF 227 (KIP), SR 1.404.

Content - Prerequisites - Script - Literature - Additional material - Exercises - Exam

The lecture course provides an introduction to field theoretic methods for systems with many degrees of freedom. A focus will be set on applications to ultracold, mostly bosonic, atomic gases, superfluids and superconductors as they are the subject of many fore-front present-day experiments. Methodologically, the lecture will introduce the basics of the operator as well as the path-integral approach to quantum field theory. In applying these techniques I will in particular concentrate on thermal and dynamical properties of the considered systems. Knowledge of the basics of quantum mechanics and statistical mechanics is presumed while the course is designed to be self-contained on the quantum-field-theory side.

  1. Introduction
  2. Introduction to quantum field theory of many-body systems
    - The quantum mechanical harmonic oscillator - Classical field theory - Fock space - Coherent states - Free systems and Wick's theorem - Cumulant expansion
  3. Mean-field theory of a weakly interacting Bose gas
    - Non-linear Schrödinger model - Bogoliubov quasiparticles - Low-energy scattering theory - Interacting ground state - SU(1,1) coherent states - Thermal Bogoliubov quasiparticles
  4. Path-integral approach to quantum field theory
    - A quick reminder of the Feynman path integral - Functional calculus - Saddle-point expansion and free propagator - Perturbation expansion, Dyson series, and resummation - Correlation functions - Connected functions and cumulants - Feynman diagrammatics - Low-energy effective theory - Linear-response theory - Retarded and advanced Greens functions - Spectral and statistical functions - Thermal path integral - *The quantum effective action - *Spontaneous Symmetry Breaking
  5. Low-temperature properties of dilute Bose systems
    - Path-integral representation of the interacting Bose gas - Ginsburg-Landau theory of spontaneous symmetry breaking - The Luttinger-liquid description and the XY model - Superfluid phase transition and spontaneous symmetry breaking - Nambu-Goldstone theorem - Superfluid phase in low dimensions - Finite-temperature superfluids - Dimensionally reduced path integral - Hydrodynamic formulation and vortices - The Berezinskii-Kosterlitz-Thouless transition - Superfluid to Mott insulator transition - *Superfluidity and superconductivity - *Anderson-Higgs mechanism

Skript :

General texts on quantum field theory Quantum optics and phase-space methods Ultracold atomic gases: General texts and theory reviews Ultracold atomic gases: A few original experimental perspectives Two-body scattering theory Non-equilibrium quantum field theory and quantum kinetic theory Additional material

Exercises will be held on Fridays, 14:15-15:45 hrs, in HS 2, INF 227 (KIP), starting on 24/10/14. Tutor: Markus Karl. (Please register here.)


Passing the written exam, which will prospectively take place on Tue., 10/02/15, 10:00-12:00 hrs, INF 227 (KIP), SR 1.404, will be the condition to obtain 8 CPs for the lecture.